# Finding roots of a polynomial

**URL:** <https://scilab.discourse.group/t/finding-roots-of-a-polynomial/200>\
**Category:** Optimization\
**Created:** [October 23, 2023, 5:51pm UTC](https://scilab.discourse.group/t/finding-roots-of-a-polynomial/200 "2023-10-23T17:51:41Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![cfuttrup](https://avatars.discourse-cdn.com/v4/letter/c/3ec8ea/32.png) [@cfuttrup](https://scilab.discourse.group/u/cfuttrup)\
**Post date:** [October 23, 2023, 5:51pm UTC](https://scilab.discourse.group/t/finding-roots-of-a-polynomial/200/1 "2023-10-23T17:51:41Z")

</div>

Dear Scilabers

I have tried to solve a polynomial for roots and find the positive (real) root.

In Python the following code works successfully:

```
import numpy as np
from scipy.optimize import fsolve

c1 = 27.9811
c2 = 30.9583

f = lambda x: x **4 - c1*x** 3 + c2*x - 1
result = fsolve(f, 1.0)
print(result) # This returns 1.0557487789221027

```

I have tried to replicate this in Scilab as follows:

```
c1 = 27.9811
c2 = 30.9583

p = %s.^4 - c1*%s.^3 + c2*%s - 1

r = roots(p, 'f')
ir = find(r==abs(r)) // find positive real root, index ir
disp(r(ir)) // This returns 27.981085, not the answer I want

```

r =

0.0211731 + 0.0243569i  
0.0211731 - 0.0243569i  
-0.0423195 + 0.i  
27.981085 + 0.i

If on the other hand I replace r = roots(p, ‘f’) with:

```
r = roots(p, 'e') // find eigenvalues

```

This returns:  
r =

27.941504 + 0.i  
-1.0484733 + 0.i  
1.0557487 + 0.i  
0.032332 + 0.i

One of these solutions is the answer I’m looing for, namely the third line (see comment in Python code).

I just wonder if anyone can explain the differences I am observing here.

The python code contains a starting estimate for fsolve (= 1.0) and finds the nearest root. Is there a similar way in Scilab?

With kind regards,  
Claus

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<div class="post-metadata">

**Author:** ![mottelet](https://yyz2.discourse-cdn.com/free1/user_avatar/scilab.discourse.group/mottelet/32/13_2.png) [@mottelet](https://scilab.discourse.group/u/mottelet)\
**Post date:** [October 24, 2023, 6:56am UTC](https://scilab.discourse.group/t/finding-roots-of-a-polynomial/200/2 "2023-10-24T06:56:28Z")

</div>

> [@cfuttrup](#):
>
> The python code contains a starting estimate for fsolve (= 1.0) and finds the nearest root. Is there a similar way in Scilab?

Yes, use Scilab,'s `fsolve`:

```auto
function y=f(x)
  c1 = 27.9811;
  c2 = 30.9583;
  y=x^4-c1*x^3+c2*x-1;
end

--> r=fsolve(1,f)
 r = 

   1.0557481

```

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<div class="post-metadata">

**Author:** ![cfuttrup](https://avatars.discourse-cdn.com/v4/letter/c/3ec8ea/32.png) [@cfuttrup](https://scilab.discourse.group/u/cfuttrup)\
**Post date:** [October 24, 2023, 5:45pm UTC](https://scilab.discourse.group/t/finding-roots-of-a-polynomial/200/3 "2023-10-24T17:45:43Z")

</div>

Hi Stéphane

Thank you. I didn’t even think to look up if Scilab has a function of the same name.

With kind regards,  
Claus